Typical = Random

This expository paper advocates an approach to physics in which “typicality” is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and are reviewed. Their original versions state that some property Φ(x) holds for P-almost all x∈X, where P probability measure on space X. more refined (and typically recent) formulations show P-random x∈X. The computational notion P-randomness used here generalizes the one introduced by Martin-Löf 1966 way now standard Examples come theory, analysis, dynamical systems/ergodic statistical mechanics, quantum mechanics (especially hidden variable theories). An underlying philosophical theme, inherited von Mises Kolmogorov, interplay between randomness, especially: comes first?